Total Completion Time Minimization Research Articles

The Study of Group Scheduling Problems with General Dual-Position-Based Job Processing Times

Scheduling with group technology has been a vivid research area in the past decades. However, group technology with general dual-effect variable processing times needs to be further explored although this kind of group technology plays an important role in some actual manufacturing scenarios. Accordingly, this paper considers group scheduling problems with a kind of general group variable processing times model, where the actual processing time of each job in group is variable due to the dual effect of both the job position and the group position. The objectives of two types of considered problems are to minimize the makespan and the total completion time, respectively. Based on the decomposition analysis, the mathematical logic analysis and the computational complexity proof, it is obtained that the makespan minimization problem and the total completion time minimization problem are both polynomially solvable under the condition that the group number is constant. For three special cases of considered problems, polynomial solving algorithms with lower computational complexity are proposed.

Total completion time minimisation of no-wait flowshop group scheduling problem with sequence dependent setup times

In this research, the no-wait flowshop sequence dependent group scheduling problem with minimisation of total completion time, noted as Fm|nwt, fmls, Splk|ΣCj is approached. A mixed integer linear mathematical model is proposed for the research problem. Due to the NP-hard nature of the proposed problem, several metaheuristic algorithms based on particle swarm optimisation and variable neighbourhood search with different neighbourhood search structures are proposed to heuristically solve the problem. Also, an efficient heuristic algorithm is proposed to generate the initial feasible solutions for the proposed algorithms. The performances of the proposed algorithms are compared with each other and the best available one in the literature by using available test problems in the literature. Based on the results, the proposed metaheuristics with structure oriented initial solutions have a better performance than the algorithms with random-generated initial solutions. [Received 14 July 2015; Revised 22 September 2015; Accepted 30 May 2016]

Scheduling with non-decreasing deterioration jobs and variable maintenance activities on a single machine

ABSTRACTThere is a situation found in many manufacturing systems, such as steel rolling mills, fire fighting or single-server cycle-queues, where a job that is processed later consumes more time than that same job when processed earlier. The research finds that machine maintenance can improve the worsening of processing conditions. After maintenance activity, the machine will be restored. The maintenance duration is a positive and non-decreasing differentiable convex function of the total processing times of the jobs between maintenance activities. Motivated by this observation, the makespan and the total completion time minimization problems in the scheduling of jobs with non-decreasing rates of job processing time on a single machine are considered in this article. It is shown that both the makespan and the total completion time minimization problems are NP-hard in the strong sense when the number of maintenance activities is arbitrary, while the makespan minimization problem is NP-hard in the ordinary sense when the number of maintenance activities is fixed. If the deterioration rates of the jobs are identical and the maintenance duration is a linear function of the total processing times of the jobs between maintenance activities, then this article shows that the group balance principle is satisfied for the makespan minimization problem. Furthermore, two polynomial-time algorithms are presented for solving the makespan problem and the total completion time problem under identical deterioration rates, respectively.

An Improved Imperialist Competitive Algorithm Based Rolling Horizon Strategy for Photolithography Machines Scheduling

This paper focuses on the photolithography machines scheduling problem in wafer fabrication factories with the objective of total completion time minimization. The operation constraints in photolithography machines include wafers arriving over time, dedicated machine constraints for critical layers, auxiliary resources constraints and unrelated parallel machines. As the problem is NP-hard and traditional scheduling algorithms cannot achieve a global optimization while considering all the constraints, an improved imperialist competitive algorithm based rolling horizon strategy is proposed. To balance the computation efficiency and optimization performance, a variable time interval approach is presented to decide the scheduling point. To search for global optima in every local schedule, the result of SRPT rule is incorporated into the local objective function. To avoid converging to local optima, an adaptive assimilation operation and a socio-political theory based competition operation are adopted in the imperialist competitive algorithm. To verify the proposed algorithm, numerical tests are conducted using historical data from a semiconductor manufacturing factory in Shanghai. Results show that the average cycle time of photo can be decreased by 14.0%.

Minimizing the total completion time on a parallel machine system with tool changes

In this paper, the identical parallel machine scheduling problem with periodic tool changes due to wear is addressed under the total completion time minimization objective. Due to machine availability restrictions induced by tool replacement operations, the problem is NP-hard in the strong sense. A mixed integer linear programming (MILP) model has been developed with the aim to provide the global optimum for small-sized test cases. Furthermore, a hybrid metaheuristic procedure based on genetic algorithms has been specifically designed to cope with larger instances. A comprehensive experimental analysis supported by a non-parametric statistical test has been fulfilled to select the best metaheuristic configuration in terms of decoding strategy and parameters driving the search mechanism as well. Then, the proposed optimization procedure has been compared with three alternative methods arising from the relevant literature on the basis of a wide benchmark of test cases. The obtained results, also supported by a proper statistical analysis, demonstrate the effectiveness of the proposed approach for solving the tool change scheduling problem at hand.

Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times

In this paper, we study a scheduling model in which the features of deteriorating jobs, serial batches, multiple job types, and setup times are considered simultaneously. In this proposed model, the jobs of each type are first partitioned into serial batches, and then all batches of different job types are processed on a single serial-batching machine. The actual job processing time is an increasing function of its starting time, and the setup time of the batches is sequence-dependent, i.e., setup time is required only when a new batch is processed first on the machine or immediately after a batch belonging to another job type. We develop optimization algorithms to solve the makespan minimization problem, the maximum tardiness minimization problem, the maximum lateness minimization problem, and the maximum earliness minimization problem, respectively. We also propose optimization algorithms to solve the problem of minimizing the number of tardy jobs under a certain agreeable condition. Finally, we discuss two special cases of the total completion time minimization problem and develop optimization algorithms to solve them.

Total completion time minimization on multiple machines subject to machine availability and makespan constraints

Abstract This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T . We study the unavailability model such that the number of available machines cannot go down by 2 within any period of p max where p max is the maximum processing time among all jobs. We show that there is an optimal polynomial time algorithm.

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

We consider the parallel-machine scheduling problem in which the machines have availability constraints and the processing time of each job is simple linear increasing function of its starting times. For the makespan minimization problem, which is NP-hard in the strong sense, we discuss the Longest Deteriorating Rate algorithm and List Scheduling algorithm; we also provide a lower bound of any optimal schedule. For the total completion time minimization problem, we analyze the strong NP-hardness, and we present a dynamic programming algorithm and a fully polynomial time approximation scheme for the two-machine problem. Furthermore, we extended the dynamic programming algorithm to the total weighted completion time minimization problem.

Scheduling jobs with position and sum-of-processing-time based processing times

The paper is devoted to some single-machine scheduling problems with variable job processing times. The objectives are to minimize the makespan (i.e., the maximum completion time of all jobs), and to minimize the total completion time. For some special cases, we show that these problems can be solved in polynomial time. For some another special cases of the makespan and the total completion time minimization problems, we prove that an optimal schedule has an V-shape property in terms of processing times. We also propose a heuristic algorithm by utilizing the V-shape property.

Scheduling a variable maintenance and linear deteriorating jobs on a single machine

We investigate a single machine scheduling problem in which the processing time of a job is a linear function of its starting time and a variable maintenance on the machine must be performed prior to a given deadline. The goals are to minimize the makespan and the total completion time. We prove that both problems are NP-hard. Furthermore, we show that there exists a fully polynomial time approximation scheme for the makespan minimization problem. For the total completion time minimization problem we point out that there exists a fully polynomial time approximation scheme for a special case.

Minimizing total completion time in the flexible flowshop sequence-dependent group scheduling problem

This research considers a flexible flowshop sequence-dependent group scheduling problem with minimization of total completion time. A mixed integer linear mathematical model for the research problem is developed. Since the research problem is shown to be strongly NP-hard, a metaheuristic algorithm based on memetic algorithm (MA) is proposed. A lower bounding method based on the Branch and Price algorithm is also proposed to evaluate the quality of the MA. In order to evaluate the performance of the proposed algorithms, random test problems, ranging in size from small, medium, to large are generated and solved by the MA and the lower bounding method. The results show that the average percentage gap of the MA is 6.03 % compared to the result of the lower bounding method for randomly generated test problems.

Single machine scheduling with sum-of-logarithm-processing-times based deterioration

In this study we consider the single machine scheduling problems with sum-of-logarithm-processing-times based deterioration, i.e., the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. We show that even with the introduction of the sum-of-logarithm-processing-times based deterioration to job processing times, single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, we show that the optimal schedule is not always V-shaped with respect to job normal processing times. Heuristic algorithms and computational results are presented for the total completion time minimization problem.

Exact and Heuristic Methods for Minimizing the Total Completion Time in Job-shops

In this paper we consider the total completion time minimization in a job-shop. We propose a new mathematical formulation based on a strip packing model. This formulation is enhanced by introducing some valid inequalities in order to compute an efficient lower bound. It is also exploited to derive an exact method; branch-and-bound algorithm which uses an improved solution of a genetic algorithm. The proposed algorithms are tested on standard benchmarks and the results are satisfactory in term of solution quality and the distance to the optimal solution.

Minimizing the total completion time in a distributed two stage assembly system with setup times

In this paper, a novel distributed two stage assembly flowshop scheduling problem (DTSAFSP) is addressed. The objective is to assign jobs to several factories and schedule the jobs in each factory with the minimum total completion time (TCT). In view of the NP-hardness of the DTSAFSP, we develop heuristics method to deal with the problem and propose three hybrid meta-heuristics (HVNS, HGA-RVNS, and HDDE-RVNS). The parameters of HGA-RVNS and HDDE-RVNS are tuned by using the Taguchi method and that of HVNS is done by using the single factor ANOVA method. Computational experiments have been conducted to compare the performances of the proposed algorithms. The analyses of computational results show that, for the instances with small numbers of jobs, HDDE-RVNS obtains better performances than HGA-RVNS and HVNS; whereas for the instances with large numbers of jobs, HGA-RVNS is the best one in all the proposed algorithms. Computational results indicate that the performances of the HDDE-RVNS and HGA-RVNS are not much affected by the number of machines at the first stage and factories. The experimental results also show that the RVNS-based local search steps in both HGA-RVNS and HDDE-RVNS are efficient and effective.

Efficient upper and lower bounding methods for flowshop sequence-dependent group scheduling problems

In this research, a permutation flowshop sequence-dependent group scheduling problem with minimisation of total completion time is considered. Since the problem is shown to be strongly NP-hard, a hybrid genetic (HG) algorithm is proposed. The only available lower bounding (LB) method for the proposed research problem in the literature based on branch and price (B&P) algorithm is also enhanced by proposing efficient method to solve sub-problems and proposing a better branching rule. A statistical comparison shows that both the proposed HG algorithm and the proposed LB have better performance than the other methods from the literature with an average 5.96% percentage gap.

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

In scheduling problems with two competing agents, each one of the agents has his own set of jobs and his own objective function, but both share the same processor. The goal is to minimize the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. In this paper we study two-agent scheduling problems on a proportionate flowshop. Three objective functions of the first agent are considered: minimum maximum cost of all the jobs, minimum total completion time, and minimum number of tardy jobs. For the second agent, an upper bound on the maximum allowable cost is assumed. We introduce efficient polynomial time solution algorithms for all cases.

The inverse parallel machine scheduling problem with minimum total completion time

In inverse scheduling problems, ajob sequence is given and the objective is to determine the minimalperturbation to parameters, such as processing times or weights ofjobs so that the given schedule becomes optimal with respect to apre-selected objective function. In this paper we study thenecessary and sufficient conditions for optimality of the totalcompletion time problem on parallel machines and inverse schedulingproblem of the total completion time objective on parallel machinesin which the processing times are minimally adjusted, so that agiven target job sequence becomes an optimal schedule.

A multi-objective genetic algorithm for yard crane scheduling problem with multiple work lines

Due to increasing ships and quay cranes, container terminals operations become more and more busy. The traditional handling based on work line is converted into pool strategy, namely loading and unloading containers with multiple work lines are operating simultaneously. In the paper we discuss the yard crane scheduling problem with multiple work lines in container terminals. We develop a multi-objective 0-1 integer programming model considering the minimum total completion time of all yard cranes and the maximization balanced distribution of the completion time at the same time. With the application of adaptive weight GA approach, the problem can be solved by a multi-objective hybrid genetic algorithm and the Pareto solutions can be finally got. Using the compromised approach, the nearest feasible solution to ideal solution is chosen to be the best compromised Pareto optimal solution of the multi-objective model. The numerical example proves the applicability and effectiveness of the proposed method to the multi-objective yard crane scheduling problem.

The two-machine flowshop scheduling problem with sequence-independent setup times: New lower bounding strategies

The two-machine flowshop environment with sequence-independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature. Nevertheless, very scant attention has been devoted to deriving effective lower bounding strategies. In this paper, we propose new lower bounds for the total completion time minimization criterion. These bounds are based on three relaxation schemes, namely the waiting time-based relaxation scheme, the single machine-based relaxation scheme, and the Lagrangian relaxation scheme. Extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time-based bounding strategy within the Lagrangian relaxation framework yields the best performance while requiring negligible CPU time.

Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times

The single-machine scheduling problems with position and sum-of-processing-time based processing times are considered. The actual processing time of a job is defined by function of its scheduled position and total normal processing time of jobs in front of it in the sequence. We provide optimal solutions in polynomial time for some special cases of the makespan minimization and the total completion time minimization. We also show that an optimal schedule to be a V-shaped schedule in terms of the normal processing times of jobs for the total completion time minimization problem and the makespan minimization problem.